Question

Stan Marsh is planning to set up a college fund for his daughter who will be heading to college 16 years from now. At that time in the future, Stan estimates that a college degree is expected to cost $ 170,630. Stan's bankinitially offered a 7.75 % interest rate annually, based on which Stan set aside some amount and readied himself to deposit into the fund. On the day of the deposit however, the bank insisted that they can only offer interest at 6.47% annually. How much more does Stan need to raise on the deposit day to still be able to financially secure his daughter's education?   

Answer 1

FV = Amount required = $170,630

r1 = interest rate = 7.75%

r2 = interest rate = 6.47%

n = 16 years

Amount required to deposit at 7.75% = FV / (1+r)^n

= $170,630 / (1+7.75%)^16

= $170,630 / 3.30123516

= $51,686.7147

Amount required to deposit at 6.47% = FV / (1+r)^n

= $170,630 / (1+6.47%)^16

= $170,630 / 2.72669188

= $62,577.661

Additional amount required on deposit day = Amount required to deposit at 6.47% - Amount required to deposit at 7.75%

= $62,577.661 - $51,686.7147

= $10,710.9463

Therefore, additional amount required on deposit day is $10,710.95